The Driving Force for the Acylation of β-Lactam Antibiotics by L,D-Transpeptidase 2: Quantum Mechanics/Molecular Mechanics (QM/MM) Study

β-lactam antibiotics, which are used to treat infectious diseases, are currently the most widely used class of antibiotics. This study focused on the chemical reactivity of five- and six-membered ring systems attached to the β-lactam ring. The ring strain energy (RSE), force constant (FC) of amide (C−N), acylation transition states and second-order perturbation stabilization energies of 13 basic structural units of β-lactam derivatives were computed using the M06-2X and G3/B3LYP multistep method. In the ring strain calculations, an isodesmic reaction scheme was used to obtain the total energies. RSE is relatively greater in the five-(1a–2c) compared to the six-membered ring systems except for 4b, which gives a RSE that is comparable to five-membered ring lactams. These variations were also observed in the calculated inter-atomic amide bond distances (C−N), which is why the six-membered ring lactams C−N bond are more rigid than those with five-membered ring lactams. The calculated ΔG ^# values from the acylation reaction of the lactams (involving the S−H group of the cysteine active residue from L,D transpeptidase 2) revealed a faster rate of C−N cleavage in the five-membered ring lactams especially in the 1–2 derivatives (17.58 kcal mol ⁻¹ ). This observation is also reflected in the calculated amide bond force constant (1.26 mDyn/A) indicating a weaker bond strength, suggesting that electronic factors (electron delocalization) play more of a role on reactivity of the β-lactam ring, than ring strain.